2. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 2
Types of Angles
An acute angle measures between 0° and 90°,
A right angle is exactly equal to 90°.
An angle greater than 90° but less than 180° is called an obtuse
angle.
A straight angle is equal to 180°.
An angle which is greater than 180° but less than 360° is called a
reflex angle.
Two angles whose sum is 90° are called complementary angles, and
Two angles whose sum is 180° are called supplementary angles.
4. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 4
Two angles are adjacent, if they have a common
vertex, a common arm and their non-common
arms are on different sides of the common arm.
vertically opposite angles formed when two lines,
say AB and CD, intersect each other, say at the
point 0 (see Fig. 3.4). There are two pairs of
vertically opposite angles.
C
5. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 5
Pairs of Angles
If a ray stands on a line, then the sum of two adjacent
angles so formed is 180°.
When the sum of two adjacent angles is 180°, then they are
called a linear pair of angles.
If the sum of two adjacent angles is 180°, then the non-
common arms of the angles form a line. This is called the
Linear Pair Axiom.
6. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 6
Theorem : If two lines intersect each other, then the vertically
opposite angles are equal
Proof : Let AB and CD be two lines intersecting at O.
13. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 13
Parallel Lines and a Transversal
A line which intersects two or more lines at distinct points is called
a transversal.
14. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL
Interior angles on the same side of the transversal
are called consecutive interior angles or allied
angles or co-interior angles
If a transversal intersects two parallel lines, then
each pair of corresponding angle is equal.
If a transversal intersects two lines such that a pair
of corresponding angles is equal then the two lines
are parallel.
15. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 15
If a transversal intersects two lines such that a pair of corresponding
angles is equal, then the two lines are parallel to each other.
If a transversal intersects two parallel lines, then each pair of
alternate interior angles is equal.
If a transversal intersects two lines such that a pair of alternate
interior angles is equal, then the two lines are parallel.
16. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 16
If a transversal intersects two parallel lines, then each pair of
interior angles on the same side of the transversal is
supplementary.
If a transversal intersects two lines such that a pair of interior
angles on the same side of the transversal is supplementary, then
the two lines are parallel.
17. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 17
• Lines which are parallel to the same line are parallel to each other.
• Note: The property above can be extended to more than two lines also.
• EXERCISE 3.2
• Find the values of x and y and then show that AB II CD.
Lines Parallel to the Same Line
25. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 25
5. If PQ || PS, PQ || SR, L. SQR = 28° and LQRT = 65°, then find
the values Of x and y.
26. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 26
5. In Fig the side QR of ∆PQR is produced to a point S. If the bisectors of
∠PQR and ∠PRS meet at point T, then prove that ∠QTR= ∠QPR.
